Nonparametric Method and Hierarchical Bayesian Approach for Parameter Estimation and Prediction
Obtaining efficient estimates or prediction from available data is one of the important goals in statistical research. In this thesis, we propose two new statistical methods to achieve this goal with examples of application and simulation studies. The parametric penalized spline smoothing (PPSS) procedure is a flexible algorithm that requires no parametric assumption and is proved to obtain more accurate estimates of curves and derivatives than available methods. In the second part of thesis, we propose a hierarchical Bayesian approach to estimate dynamic engineering model parameters and their mixed effects. This approach has the benefit of accurately estimating unidentifiable parameters from right censored data. It is further investigated with simulated data to perform predictions. Predicting quality with this method is proved to be better than that from procedures without considering censoring situation.
Supervisor: Charmaine Dean